The problem now was at the 3rd line of the status: DOWN
This means that the bluetooth dongle itself is installed properly and the system recognizes it. However it is not running. There are a bunch of things one can do in this case, but all resulted in errors:
# hciconfig hci0 up
Can't init device hci0: Device or resource busy (16)

After a while I decided to isolate the problem, ripped all my other USB devices off and restarted the RPi. It turned out that my wireless keyboard (Logitech K400) was disturbing the Bluetooth dongle. Seems as if Linux isn’t good at handling different devices that are communicating wireless (both via Bluetooth).

The solution now is to not use the wireless keyboard anymore. Instead I’m using a wired keyboard if needed. I’m currently working on getting rid of the keyboard in RetroPie anyways, more on that in the next days.

You’re right, in the end there are two bluetooth receivers, even if the Logitech receiver does not say that it is. I’ve got no success using the keyboard with the Bluetooth dongle or the gamepads with the Logitech dongle.

However I found that there are more people having problems with their dongle not getting up and running, so I thought it would be a good idea to share what worked for me. There are still some problems uncovered regarding Raspberry Pi and emulation on it in particular.